Explanation:

To find the order of the group G / AB, we need to understand the properties of normal subgroups and the concept of factor groups.

1. Normal Subgroups:
A normal subgroup is a subgroup that is invariant under conjugation by members of the group. In other words, if N is a normal subgroup of a group G, then for any element g in G and n in N, the conjugate of n by g, gng^(-1), is also in N.

In this question, A and B are given as normal subgroups of G.

2. Factor Groups:
The factor group G / N, where N is a normal subgroup of G, is the set of cosets of N in G, with the group operation defined as (aN)(bN) = (ab)N for all a, b in G.

In this question, we need to find the order of the factor group G / AB.

3. Order of a Factor Group:
The order of a factor group G / N is given by the formula: |G / N| = |G| / |N|.

In this question, we are given that the order of G is 30, the order of A is 2, and the order of B is 5. We need to find the order of G / AB.

4. Order of G / AB:
Using the formula for the order of a factor group, we can substitute the given values to find the order of G / AB:

|G / AB| = |G| / |AB|

Since A and B are normal subgroups, their intersection AB is also a normal subgroup of G. And the order of AB can be found using the formula for the order of the product of two subgroups:

|AB| = |A| * |B| / |A ∩ B|

In this case, |A ∩ B| = 1, since the only common element of A and B is the identity element. Therefore, |AB| = |A| * |B| = 2 * 5 = 10.

Plugging this value into the formula for the order of the factor group, we get:

|G / AB| = |G| / |AB| = 30 / 10 = 3

Therefore, the order of the group G / AB is 3.

Hence, the correct answer is option 'B'.